Goals: To help you understand the relationship between the angular size (in degrees, arcmin, or arcsec), physical size (in km or miles) and distance of an object (in km or miles), and to help you discover the mathematical relationship between them. Astronomers use the resulting formula to determine the physical sizes of planets and moons -- it is a key source of observational information in astronomy.
1) In words, describe how the appearance of the planet -- specifically, its angular diameter -- changes as you get closer.
2) Is the physical size of the planet (that is, its diameter measured in km or miles) changing as you approach? Explain.
3) Enter your measurements in the table below, and plot the data on the graph (notice units). Connect the points on your graph with a smooth curve.
4) Which of the functions looks the most like the curve you plotted?
5) On the curve you plotted on the opposite side of this paper, the x-axis measures the quantity _________________, while the y-axis measures the quantity ___________________. Substitute these quantity names into the equation you selected in Question 4 to define a new equation that describes what you observed in the movie:
But wait, the equation as we wrote it isn't quite correct -- plug in some numbers and see (e.g., 1 / 2x106 is not 20!). In our next class we will discuss what is still missing from this formula. Then we will expand it to include the physical size of the object and practice using the formula to determine the physical size (in km) of some astronomical objects.